Modeling the Dynamics of Covid-19: Model With Patients With Underlying Conditions

Abstract

Introduction : Coronavirus disease (COVID-19) is an infectious disease caused by the SARS-CoV-2 virus. The virus can spread from an infected person’s mouth or nose in small liquid particles when they cough, sneeze, speak, sing or breathe. These particles range from larger respiratory droplets to smaller aerosols. Objective: The study aims to formulate a deterministic model to understand the dynamics of SARs Corona Virus infection among the Kenyan population with a vital interest in two proportions; people with other chronic illnesses and those who do not have other chronic illnesses. Methodology: We formulate, study and analyze a deterministic model of COVID-19 transmission dynamics with eight compartments. Here, we use a system of non-linear ordinary differential equations with optimal control and three therapeutic measures, which include vaccination of the Susceptible proportion, treatment at the hospital, and homebased care mitigation and treatment. This system has disease-free and endemic equilibrium points whose stability is investigated. The basic reproduction number, R0, is calculated using the next-generation matrix. The disease-free equilibrium, DFEq of the model is asymptotically stable if R0 < 1 and unstable if R0 > 1 whereas endemic equilibrium, EEq of the model becomes asymptotically stable if R0 >1. Sensitivity analysis was performed on all parameters to determine their impact on the transmission of COVID-19. Finally, the parameter estimation was conducted, and numerical simulation of the model using MATLAB and graphs were shown. Results: A basic reproduction number,R0=1.35, indicating that COVID-19 will persist within the population. Results from the simulation suggest that low adherence to the measures put in place to curb the disease increases infection in the population. Hospitalization and home-based care programs show that an increased rate of hospitalization and care lowers infection.